Unfortunately in our rescue, we've seen a lot of cross-species injuries, primarily between guinea pigs and rabbits, mainly because those are more common.
Primarily we see old, healing fight wounds, some broken ribs and spinal damage. We do see a of suspected malnutrition deaths -- liver failure and hind end paralysis in guinea pigs eating rabbit food, blindness and eventual death in rabbits eating pig food.
The case of Gumbo the Guinea Pig is pretty consistent with what we see from guinea pigs and rabbits whose ignorant owners assure us that they're "best friends":
The Case of Gumbo the Guinea Pig - or Why Not to House Rabbits with Guinea Pigs - Guinea Pig Cages Forum
Saddest to watch are those who don't really have 'problems'. Watching a lonely rabbit demand grooming over and over again from a guinea pig who has no idea what the rabbit wants (guinea pigs do not socially groom).
There was a horrific case I saw online where wild rats had vicious attacked a guinea pig who was living out in a shed. Though domestic rats are obviously not wild, it was heartbreaking to hear of the damage to the poor guinea pig, and a good warning.
In the end, it seems like a disservice to the animals you've taking into your guardianship to put them with another species for the owner's convenience.
I suspect that we would see more chinchilla, degu, ferret, and sugar glider problems if they were not so expensive. More often than not, owners will simply sell them from person to person to recoup their money, rather than turning them over to a rescue to find a suitable home for them.